anonymous
  • anonymous
Please help :0 Find the term containing x^42 of (x^3-3)^16
Mathematics
katieb
  • katieb
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
well first we need \(\frac{42}{3}=14\) to know which term we want
anonymous
  • anonymous
so it is either the 14th term or the second term depending on how you are counting. makes no difference. the term looks like \[\dbinom{16}{2}(x^3)^{14}(-3)^2\]
anonymous
  • anonymous
\[\dbinom{16}{2}=\frac{16\times 15}{2}=8\times 15=120\] and \((-3)^2=9\) multiply to get your answer

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anonymous
  • anonymous
wow my drawing really sucked.... oh well!!
anonymous
  • anonymous
Thanks so much satellite73!

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